Structures and relative stabilities of small Con clusters (n = 1-12) on a Cu(111) surface are studied using molecular dynamics simulations. It is shown that the supported clusters are all in two-dimensional island structures of the edges forming square microfacets (A step) and/or triangular microfacets (B step) with the substrate. For non-magic-number clusters, the lowest energy structures are the ones of the edges with more A steps and the most unstable structures are the ones of the edges with only A steps or B steps due to the lattice mismatch of the Co-n/Cu(111) system. Magic number clusters are truncated triangular or elongated shapes with a closed atomic shell and maximum nearest-neighbor bonds. In addition, the anomalous mobility is found for Co-3 and Co-6 clusters in the diffusion processes of these clusters. The concerted translation and rotation movements are responsible for their special diffusion behaviors. (C) 2017 Elsevier B.V. All rights reserved.